The Owls suffered a seventh straight defeat as late goals from Sam Baldock (pen) and Albert Adomah saw the Robins come from behind to silence the home fans.
Gary Madine thought he'd grabbed a dramatic equaliser at the death with what would have been his second of the afternoon, but referee Andre Marriner ruled it out with Llera trying to confront him for not awarding a penalty in the build-up.
Llera's resulting booking and the Owls' defeat completed a sour turnaround for the defender, who had put the hosts in front in just the third minute with a well-placed header.
Jones said afterwards: "There are things that go against you, I have seen the referee and he says that Llera has pushed him. If he has pushed him, that's the stupidity of it.
"He says he didn't so, if he didn't then the referee has made a decision I have never seen before in football. It was a clear-cut penalty, but he didn't see it.
"Miguel should have carried on playing - the ball was still alive, he is not going to change his mind and he ran at him.
"I don't see any movement from the referee, but that's what happens sometimes when you are down there. We were winning the game 2-1 and should have had more goals but that composure is just missing.
"Today was a prime example of, 'When your luck is out, it's out', which is silly because for 84 minutes our luck was in. But it's cost us."
On his uncertain future as manager of Wednesday, Jones added: "I see the chairman every day. I am going up to see him now to talk about the game, I just wish the referee was sat there with me."